As an Italian 100% living in Rome I feel obliged to clarify this.
Madonna's real name is Veronica Ciccone. She has Italian origins, but she is American (meaning, born in the US, not here in Italy). Her parents were born in Pacentro, a small village few km from my home town, L'Aquila, which is in its turn 100Km far from Rome (60 miles, more or less, if I am not mistaken).

Madonna is a exclusively Christian RELIGIOUS name, meaning EXCLUSIVELY "Holy Virgin", and it is definitely NOT a common first name for a woman. When she became popular world wide, she definitely had a "scandalous" name, in "Catholic" terms, here in Italy, since nobody would dare, and actually even think, to use such a name as an artistic name. That would exactly be as using the name "God" (Dio, in Italian) for a male singer or, even more unusual, for your son! Actually, you never can tell, people give their children strage and unusual names, but I have never heard of a woman named "Madonna", as well as I have never heard of a man named "God", or "Christ", or "Saint Joseph". :)
I have to say that, although a child, I myself was a bit shocked when I heard of a singer named "Madonna", and I still remember all the debates and polemics on some talk shows, magazines, newspapers here in Italy. I mean, try to imagine what it means to see a pretty sexy and trasgressive singer singing "Like a Virgin" and "Material Girl" named "Holy Virgin". And rememebr that "Madonna" is still today used in an exclusively religious sense, not for anything else!!! .

And now consider, even to that "technically" blasphemous usage of the therm "Madonna" we got totally used, and now she is just considered an artist who tryed to shock the audience, as usual. Not a big deal at all anymore. This is a proof of how things change, and how rapidly.

For those who are interested, "Madonna" comes from the Latin "Mea Domina", meaning, literally, My Lady, same origns and meaning as "Madame" in French.